Suppose that in Country A, a small open economy, there is a positive shock to the propensity of consumers to save: for the same world real interest rate, all of a sudden people are willing to save more.
If the world real interest rate is unchanged...

the Current Account Balance of Country A will improve

the Current Account Balance of Country A will deteriorate

the Current Account Balance of Country A will deteriorate if it's running a surplus, improve if it's running a deficit

the Current Account Balance of Country A will improve if it's running a surplus, deteriorate if it's running a deficit

As for the provided information the citizens of the country will save more as there is a positive shock. Accordingly the citizens shall save more, as the real is not changed the balance due to savings will increase of the current accounts.

This is reflected clearly in statement 1, this is because with the same real rate of interest the balance will increase, of current accounts and as a result it will improve.